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A140969 Prime numbers whose hexadecimal representation uses only the digits A,B,C,D,E,F (and not the decimal digits).

%I A140969 #23 Aug 31 2025 21:02:26
%S A140969 11,13,173,191,223,239,251,2731,2749,2767,2797,3019,3023,3037,3067,
%T A140969 3259,3307,3323,3499,3517,3533,3547,3581,3583,3803,3821,3823,4013,
%U A140969 4027,4079,4091,4093,43691,43711,43759,43951,43963,43997,44027,44029,44203,44207
%N A140969 Prime numbers whose hexadecimal representation uses only the digits A,B,C,D,E,F (and not the decimal digits).
%H A140969 Charles R Greathouse IV, Nov 16 2009, <a href="/A140969/b140969.txt">Table of n, a(n) for n = 1..10000</a>
%e A140969 11=B 13=D 113=AD 131=BB
%t A140969 Select[Prime@ Range[5000], Min[IntegerDigits[#, 16]] > 9 &] (* _James C. McMahon_, Jul 15 2025 *)
%o A140969 (PARI) mindigit(n,b) = if(n<b, n, min(mindigit(floor(n/b),b),n%b))
%o A140969 isA140969(n) = (isprime(n) && mindigit(n,16) > 9) \\ _Michael B. Porter_, Dec 01 2009
%o A140969 (Python)
%o A140969 from sympy import isprime
%o A140969 from itertools import count, islice, product
%o A140969 def agen(): # generator of terms
%o A140969     yield from (t for d in count(1) for r in product("ABCDEF", repeat=d-1) for e in "BDF" if isprime(t:=int("".join(r)+e, 16)))
%o A140969 print(list(islice(agen(), 44))) # _Michael S. Branicky_, Aug 31 2025
%Y A140969 Cf. A238090.
%K A140969 base,nonn,changed
%O A140969 1,1
%A A140969 _Gil Broussard_, Jul 27 2008
%E A140969 Edited by _N. J. A. Sloane_, Nov 15 2009